Linear systems with hyperbolic zero dynamics admit output regulator rejecting unknown number of unknown sinusoids

This study presents an off‐the‐shelf error feedback controller that can completely rejects the sinusoidal disturbances whose magnitudes, phases, bias, frequencies and even the number of frequencies are all unknown. A closed‐form solution is given under the assumptions that the plant has no uncertainty and has hyperbolic zero dynamics (i.e. there is no zero on the imaginary axis of the complex plane), and that the number of unknown frequencies has upper bound which is known. A non‐minimum phase plant can be dealt with. The proposed controller is tested by a simulation, which verifies its effectiveness.